Question

Assertion :At depth $h$ below the water surface pressure is $P$. Then at depth $2h$ pressure will be $2P$. (Ignore density variation). Reason: With depth pressure increases linearly.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Both Assertion and Reason are incorrect

Answer 1

The correct option is D Both Assertion and Reason are incorrect

Given : $P_A=P$

Let the atmospheric pressure be $P_o$

$\therefore$ Pressure at point A $P_A=P_o+\rho gh$

OR $P=P_o+\rho gh$ $⟹\rho gh=P-P_o$

Pressure at B $P_B=P_o+\rho g\left(2h\right)=P_o+2P-2P_o=2P-P_o$

$⟹$ $P_B\ne 2P$

Hence the pressure doesnot increase linearly with depth.

Thus the assertion as well as the reason statements are incorrect.